Research Projects

Ultracold atomic gases in optical lattices offer a platform for simulating complex quantum many-body systems in condensed matter physics. These systems, which are non-Hermitian due to coupling with external degrees of freedom, violate the conservation principle, leading to non-reciprocal tunneling or dissipation. This non-reciprocity is common in nature and can lead to intriguing emergent features. The project aims to examine the localization of non-Hermitian quantum many-body systems, exploring the interplay of the non-Hermitian skin effect and stark MBL. Numerical tools will be developed using the quantum trajectory approach to investigate the dynamic evolution of non-Hermitian systems. Due to the growing Hilbert space dimension with system size, the Hamiltonian matrix of larger sizes will need to be diagonalized, which is not feasible on a standard desktop computer. High-performance computing facilities will be required for the numerical simulations. The project also explores spin-orbit coupled systems in optical lattices, which are ideal proxy for topological phases of matter, Weyl semimetals, spintronics-based devices, and finite-momentum superfluidity. The study will investigate the effect of disorder and explore the possibility of novel glassy phases. The spin-orbit coupled bosons with long-range dipolar interactions could lead to chiral supersolid, superstripe, and quasicrystal states. The proposed research plan serves as a foundation for further theoretical investigations and will be useful in designing future experiments.